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klemol [59]
2 years ago
11

Which of the following is a true proportion of the figure based on the triangle

Mathematics
1 answer:
Anni [7]2 years ago
4 0

Based on the triangle proportionality theorem, the true proportion is h/j=k/i

<h3>How to solve for the true proportion</h3>

In the diagram that we have here, we have TU to be parallel to QR.

We have following

ST is equal to h, TQ is equal to j, SU is equal to k and UR is equal to i.

This can then be used to form the equation

ST/TQ = SU/UR

When we h/j = k/i

Read more on proportionality here:

brainly.com/question/20384391

#SPJ1

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3 years ago
Do the points (−1,9) and (2,4) represent the vertex and a sample point, respectively, of y=−2(x+1)2+9? Explain
Reil [10]

Answer:

Vertex: (-1,9) is true

Sample Points: (2,4) is not true

Step-by-step explanation:

Given

Vertex: (-1,9)

Sample\ Points: (2,4)

Required

Determine if the vertex and sample points exist for y= -2(x+1)\²+9

Solving for the vertex:

y= -2(x+1)\²+9

Writing the given equation in the form:

y = ax^2 + bx + c

Expand the bracket

y= -2(x+1)(x+1)+9

Open Bracket

y= -2(x+1)(x+1)+9

y = -2(x^2 + 2x + 1) + 9

Open bracket

y = -2x^2 - 4x -2 + 9

y = -2x^2 - 4x +7

Solve for x using:

x = \frac{-b}{2a}

Where a = -2; b = -4;

<em>So:</em>

x = \frac{-(-4)}{2 * (-2)}

x = \frac{4}{-4}

x = -1

Substitute -1 for x in y = -2x^2 - 4x +7

y = -2(-1)^2 -4(-1) + 7

Simplify all brackets

y = -2(1) + 4 + 7

y = -2 + 4 + 7

y = 9

Hence;

<em>The vertex (x,y) is (-1,9)</em>

<em>This is true</em>

Checking sample points: (2,4)

In this case; x = 2 and y = 4

Substitute x = 2 and y = 4 in y= -2(x+1)\²+9

4 = -2(2 + 1)^2 + 9

4 = -2(3)^2 + 9

4 = -2 * 9 + 9

4 = -18 + 9

4 \neq -9

<em>Hence;</em>

<em>This sample points </em>(2,4)<em> does not exist</em>

8 0
3 years ago
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